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Existence of Limit

Solve using L...

Question

Solve using L' Hospital Rule
$lim n \to \infty \frac{x - x 2^{2}}{3 x^{2} + 5 x}$

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Solution

$ν x \to \infty \frac{x - 2 x^{2}}{5 x}$ as $\frac{\infty}{\infty}$ form use L hospital
$= \frac{1 - 4 x}{x + 5}$ still $\frac{\infty}{\infty}$
$= \frac{- 4}{6} = \frac{- 2}{3}$

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